I just got hired to start teaching the past month. This is my first real teaching experience. And so far it’s been okay for the most part. I have a really good handle on the higher grades and feel like I connect with the kids well. I’m even doing alright with the first and second graders, and feel like I’m learning a lot

But my third grade is a disaster. Some of the kids don’t stay in their seat at all, they’re even worse than the first graders. Some of them are very loud and disruptive. They’re very rude and have even began to annoy the good students

One of the 3rd grade classes is manageable since there is only about 2 or 3 troublemakers. So it’s easy to isolate the bad ones. But the other class legitimately has 6 or 7 problematic kids. Once a few start acting out, easy to lose control of the entire class.

What are some techniques I can use to manage the problem class? I can’t really yell at them or send them to the principals office unless they do something extremely crazy. Really feels like my hands are tied

Damn, I read the other person's post and now they deleted it, but they had a load of decent suggestions to help you.  Not sure why they deleted.  Will try and remember some of the things they wrote.

The main thing to remember is to be consistent.  If you start a method to control the students you have to maintain it.  It is not going to be an easy fix and can take a few weeks to see some small results, but once you start to appeal to some of the trouble makers then you'll slowly draw the others in to.  But you need to keep at it.

I had the same thing as you when I first came to Korea.  One of my elementary schools had a really good 3rd/4th and 5th grade, but the 6th grade were awful.  Their homeroom teacher was an older guy in his late fifties and he used to disappear out the door for a forty-minute smoking break when I walked in.  They gave me no end of trouble.  So I tried different things.

First, I found out their names. It is much easier to identify and scold someone if you use their name.  It may take time but knowing the students names in any school is most important.
 
Second, the other person wrote about the 'naughty box'.  If there are students who keep acting up put their name in the box.  Korean students on the whole don't like to be singled out and have their names on the board in a box saying they're bad.  There is the added thing of them not knowing what you'll do if they make it to break-time and their name is still in the box.  If you have a friendly teacher from another class, escort that child to them to tell them off during break time.  If they're good or do something good then they get their name erased.  It is important to be consistent and show that being good means something.

Third, like the other person wrote, have a box in the corner of the board.  If somebody does something bad or they talk when you talk, put a mark in the box.  Each mark means a minute off their break-time.  Doing something good, will get the mark erased.  You don't need to raise your voice, just look like you'll put a point in the box and usually they'll self-police.  If you do this then you need to follow through with it.  The first time might have a few points but you need to show you mean business.  You can have three minutes of silence, and you watch them, if anyone makes a peep then you restart the time.  You can make them memorise a sentence and then they all have to come to you and recite it.  There are a few different things to do here. 

Fourth, if you are able to you can move the students places, so the troublemakers are not together.  I know this is more difficult in elementary school as students are usually assigned desks.  This way also helps you with their names as you can have a seat plan in front of you.  Once you take the power away from the students about where they can sit it gives you more of it.  It shows you have the control.  I used to teach one very boisterous boy so I used to surround him with girls.  He made a peep, they fixed him.     I don't have to do anything. 

Fifth, you could try stickers.  Make a point that participation will get them some candy or something.  Make a star chart with the students names on.  If they give good answers, then they get a star.  If the troublemakers get stickers then usually they don't want to lose them.  Making a point of praising them for getting stickers.  The better students will naturally get stickers so make a point of giving them candy if say, they get five stickers.  Over time, a lot of students will have stickers so if they are bad, then you can remove one or two from everyone.  With this one you have to be very consistent. 

I'm sure others can chime in.  I know Chinguetti usually has some very good ideas about controlling elementary kids.  But like i said, don't expect results straight away.  Choose some systems and make sure you are consistent with it. 

OP, I suggest using their valuable time against them. Basically any time a student(s) acts out, add 30 seconds on the board. Once class is over, the time on the board represents how long they have to sit in their seats during break time (10 minutes at my school).  Students generally cherish this time because they get to play with their friends during break time. I find taking that time away from them really helps with keeping the class in line. I usually do this for the entire class but can be done for individual students if you can keep track of each student. It worked for my 5th/6th graders. Not sure how it will translate for 3rd graders but you might as well try. FYI, this timer is talked about on the first day of classes so students know what to expect.

I got this from a poster on Waygook actually so I can't claim it (props to whoever made this!!!), but it's a really, really good system. I don't like singling kids out because it doesn't seem as fair and some get upset if they don't get stickers or prizes, so this year I started with this. I only have one or two really bad classes behavior-wise but haven't had to use the Red Cards yet. Seems like a pretty good and fair system though.

Also, what worked for me last year if they were acting up, was I wrote GAME on the board. If they were acting out, I erased a letter. Of course, if I erase everything in one day, that means no game. That really really seemed to quiet them down.

To that I would add, fairness.

Absolutely.  As important as the others.   

It's tricky with classes that people write about on here, because nobody can really know another person's situation, although we've all had similar sounding situations and dealt with them in our own ways.  What might work with one class may not work so well with another.  With the OP having seven students acting out, by being tough with the whole class, and having a decent 'carrot', it sounds like you can win them over slowly, leaving one or two acting up, who may just give up acting out at all.  But it's horses for courses, really.  But to stick it out is the most beneficial thing and not to expect instant results. But over time, I think it makes much better teachers out of us all, adds strings to our bow, and helps us develop personally. 

Try not to lose heart a month in.  You're still finding your feet so at the moment it is trial and error.  I remember deciding never to play bingo with my elementary kids because on the few occasions I played it, there were always tears from the 'losers'.  Not worth the hassle.  You'll find what is best for each group, but it takes time.

It's Friday, so take your mind off it and enjoy the weekend. 

Try not to lose heart a month in.  You're still finding your feet so at the moment it is trial and error.  I remember deciding never to play bingo with my elementary kids because on the few occasions I played it, there were always tears from the 'losers'.  Not worth the hassle.  You'll find what is best for each group, but it takes time.

It's Friday, so take your mind off it and enjoy the weekend. 

Thank you for saying that, really needed to hear it!

You're right, shouldn't think too much about it. Best thing to do is forget all about work and come back next week with a fresh start. Eternal sunshine of the spotless mind